On the high-density expansion for Euclidean random matrices

Autores
Grigera, Tomas Sebastian; Martín Mayor, V.; Parisi, G.; Urbani, P.; Verrocchio, P.
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series,allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
Fil: Grigera, Tomas Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Martín Mayor, V.. Universidad Complutense de Madrid; España
Fil: Parisi, G.. Università degli Studi di Roma "La Sapienza"; Italia
Fil: Urbani, P.. Università degli Studi di Roma "La Sapienza"; Italia
Fil: Verrocchio, P.. Universita degli Studi di Trento; Italia
Materia
EUCLIDEAN RANDOM MATRICES
HIGH-DENSITY EXPANSION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/271469
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the high-density expansion for Euclidean random matricesGrigera, Tomas SebastianMartín Mayor, V.Parisi, G.Urbani, P.Verrocchio, P.EUCLIDEAN RANDOM MATRICESHIGH-DENSITY EXPANSIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series,allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Fil: Grigera, Tomas Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Martín Mayor, V.. Universidad Complutense de Madrid; EspañaFil: Parisi, G.. Università degli Studi di Roma "La Sapienza"; ItaliaFil: Urbani, P.. Università degli Studi di Roma "La Sapienza"; ItaliaFil: Verrocchio, P.. Universita degli Studi di Trento; ItaliaIOP Publishing2011-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/271469Grigera, Tomas Sebastian; Martín Mayor, V.; Parisi, G.; Urbani, P.; Verrocchio, P.; On the high-density expansion for Euclidean random matrices; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2011; 2-2011; 1-381742-5468CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://stacks.iop.org/1742-5468/2011/i=02/a=P02015info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2011/02/P02015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:05:52Zoai:ri.conicet.gov.ar:11336/271469instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:05:52.966CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the high-density expansion for Euclidean random matrices
title On the high-density expansion for Euclidean random matrices
spellingShingle On the high-density expansion for Euclidean random matrices
Grigera, Tomas Sebastian
EUCLIDEAN RANDOM MATRICES
HIGH-DENSITY EXPANSION
title_short On the high-density expansion for Euclidean random matrices
title_full On the high-density expansion for Euclidean random matrices
title_fullStr On the high-density expansion for Euclidean random matrices
title_full_unstemmed On the high-density expansion for Euclidean random matrices
title_sort On the high-density expansion for Euclidean random matrices
dc.creator.none.fl_str_mv Grigera, Tomas Sebastian
Martín Mayor, V.
Parisi, G.
Urbani, P.
Verrocchio, P.
author Grigera, Tomas Sebastian
author_facet Grigera, Tomas Sebastian
Martín Mayor, V.
Parisi, G.
Urbani, P.
Verrocchio, P.
author_role author
author2 Martín Mayor, V.
Parisi, G.
Urbani, P.
Verrocchio, P.
author2_role author
author
author
author
dc.subject.none.fl_str_mv EUCLIDEAN RANDOM MATRICES
HIGH-DENSITY EXPANSION
topic EUCLIDEAN RANDOM MATRICES
HIGH-DENSITY EXPANSION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series,allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
Fil: Grigera, Tomas Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Martín Mayor, V.. Universidad Complutense de Madrid; España
Fil: Parisi, G.. Università degli Studi di Roma "La Sapienza"; Italia
Fil: Urbani, P.. Università degli Studi di Roma "La Sapienza"; Italia
Fil: Verrocchio, P.. Universita degli Studi di Trento; Italia
description Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series,allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
publishDate 2011
dc.date.none.fl_str_mv 2011-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/271469
Grigera, Tomas Sebastian; Martín Mayor, V.; Parisi, G.; Urbani, P.; Verrocchio, P.; On the high-density expansion for Euclidean random matrices; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2011; 2-2011; 1-38
1742-5468
CONICET Digital
CONICET
url http://hdl.handle.net/11336/271469
identifier_str_mv Grigera, Tomas Sebastian; Martín Mayor, V.; Parisi, G.; Urbani, P.; Verrocchio, P.; On the high-density expansion for Euclidean random matrices; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2011; 2-2011; 1-38
1742-5468
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://stacks.iop.org/1742-5468/2011/i=02/a=P02015
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2011/02/P02015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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